Translation by a vector in the coordinate plane is first introduced in precalculus and connects to the basic theory of vector spaces in linear algebra. In this article, the authors explore the topic of collision detection in which the idea of a translation vector plays a significant role. Because collision detection has various applications in…

What does it mean for teachers to integrate technology effectively? Effectively integrating technology means teaching "with" not "near" technology. The author defines "teaching near technology" (Leatham 2002) as using technology in a manner that does not promote opportunities for students to communicate, reflect, and…

The correct use of visual perspective is one of the main reasons that virtual reality environments and realistic works of art look lifelike. Geometric construction techniques used by artists to achieve an accurate perspective effect were developed during the Renaissance. With the rise of computer graphics, translating the geometric ideas of 600…

The authors provide a dynamic Ferris wheel computer activity that teachers can use as an instructional tool to help students investigate functions. They use a student's work to illustrate how students can use relationships between quantities to further their thinking about functions.

In the criminal justice system, defendants accused of a crime are presumed innocent until proven guilty. Statistical inference in any context is built on an analogous principle: The null hypothesis--often a hypothesis of "no difference" or "no effect"--is presumed true unless there is sufficient evidence against it. In this…

To create an environment in which all students have opportunities to notice, describe, and wonder about variability, this article takes a context familiar to many teacher--sampling colored chips from a jar--and shows how this context was used to explicitly focus on variation in the classroom. The sampling activity includes physical as well as…

The Wednesday before Thanksgiving presents a challenge to teachers in many U.S. schools. Some students are absent because they are traveling to be with their extended families for the holiday. Other students, assuming that nothing important will happen at school when so many of their peers are absent, may also be absent. One school's solution to…

Played in university classes for preservice teachers as well as in middle and high schools, the River Crossing Game depends on the sum of tosses of two fair dice. This paper describes the game as well as some lines of thinking about winning strategies, which are not obvious even with an understanding of the overall distribution for the sum of two…

This article describes an activity that involves the use of simulation for decision-making. It is useful for demonstrating concepts in probability and statistics. (Contains 4 figures and 2 tables.)

Discusses the use of the mathematics classroom for discovering the relationship among computers, mathematics, and real-world problems. Provides three probability problems and compares the results of three methods, actual trial, computer simulation, and mathematical solution. (YP)